I have a conjecture:
Any odd positive number is the sum of 2 to an i-th power and a
(negative) prime.
2n+1 = 2^i+p
for example: 5 = 2+3 9=4+5 15=2^3+7 905=2^12-3191 ....
as to 2293=2^i +p $B!$(BI don't know i , p . it is sure that i>30 000 if
the conjecture is correct.
More,
n = 3^i+p, (if n=6k-2 or n=6k+2)
for example:8 = 3+5 16=3^2+7 100=3+97, 562 = 3^6 -167
I can't proof this. Do you have any idea?